FRISCO, Texas -- Owner and general manager Jerry Jones wants Cooper Rush to make life difficult for the Dallas Cowboys.

He wants Rush, the backup quarterback, to play so well that there would be controversy as to whether Dak Prescott would assume the starting role once he is healthy enough to play after undergoing right thumb surgery last week.

"Of course I would. Of course. That means we'd have won," Jones said. "If he comes in there and plays as well as Prescott played, Rush? Played that well over these next games ahead? I'd walk to New York to get that."

As Jones spoke, thoughts of 2016 emerged. Prescott was a rookie fourth-round pick that year, filling in for an injured Tony Romo, who hurt his back in a preseason game. After losing the season opener that year, the Cowboys won a franchise-record 11 straight games and Romo never regained his starting position. Can Rush do that?

"Well, I don't know that," Jones said. "You can't find on record where I said I thought Dak Prescott could do it when he stepped in and had the chance to do that. But he did it."

Rush will make his second straight start on Monday against the New York Giants and just the third of his career. The Cowboys have won both of Rush's starts on final-minute drives, including winning on a 50-yard field goal to beat the Cincinnati Bengals 20-17 last week.

There is one flaw in Jones' thought process. Unlike with Romo's injury when the Cowboys knew he would miss a couple of months, Jones believes there is a chance Prescott returns Oct. 2 against the Washington Commanders.

"Well, of course we want Dak to be here next week," Jones said. "That's the thing. You do. But Dak and I want Rush to lead the team to a victory here and get another win and get another win. That's the only way to look at it. Looking back when Dak was playing instead of Tony, it was game by game. It wasn't the long look we had after two months to look back. It was actually play by play, almost series by series. So do I think that it's possible for Rush to come in here and play at a level to win games the way Prescott did when he took over for Romo? Yes I do. Yes I do. I certainly think that's possible."

Prescott has yet to have the stitches removed from his thumb. He went through rehab and conditioning work during the portion of Thursday's practice that was open to the media.

In the immediate aftermath of the season-opening loss to the Tampa Bay Buccaneers, sources said Prescott would miss 6-8 weeks, however the club received favorable news from the surgeon that it could be a four-week absence, if not sooner.

"I will tell you that it won't be because anybody is worried about that getting hurt [again]," Jones said. "If we're worried [it's] because of his grip and the strength in his grip. But is it possible for him to play within four weeks and sleep at night with him getting hurt or not getting hurt, the answer is yes."

But back to the possibility of Rush being more than a caretaker. When asked about outside narratives that Prescott needs to study Rush's tape, Ezekiel Elliott smirked.

"It's just really people on TV to get clicking, to get views, they're going to say the most outrageous stuff and you're going to get the most attention. That's their job. Who knows if they really believe it?"

But what about when Jones says he hopes to have a "dilemma," when Prescott is healthy?

"He wants y'all to be licking and listening to him too," Elliott laughed. "It's all marketing, man. It's all marketing."